Chapter 7. ElectrodynamicsProblem 7.2

Two metal objects are embedded in weakly conducting material of conductivity ?. Show that the resistance between them is related to the capacitance of the arrangement by

Suppose you connected a battery between 1 and 2 and charged them up to a potential difference V0. If you then disconnect the battery, the charge will gradually leak off. Show that V(t) = V0 exp(-t/?), and find the time constant ? in terms of ?0 and ?.